The most popular method of "flipping a coin" without a coin involves just a little bit of elementary math.
  1. Each person (normally two, but more can take part) picks either the number one or two.
  2. Each person holds that many fingers up behind their back.
  3. On the word "go", each person pulls their hand from behind their back.
  4. The number of fingers are added. If the sum is an even number, it's tails. If an odd number, it's heads.

No matter which number you yourself pick, the second person has an equal chance of making the sum even or odd -- as does the third, fourth, or nth person taking part.